Why do AC Vents stayed closed on 1998 Buick LeSabre?

The vent control mechanism is powered by engine vacuum. Start the engine and let it idle while you open the hood and listen for the tell-tale hissing sound of an open vacuum line. Once you find the loose hose/tube, it's just a matter of finding the orifice to which it belongs and plugging it back there. If the hose/tube is damaged, repairs might first need to be done before they can be inserted back and stay attached.

There are also vacuum lines controlling the vents behind the glove box, here is a link to a site that will help you with that side of the troubleshooting.